Centimeter-scale hole diffusion and its application in organic light-emitting diodes for reducing eciency roll-off and enhancing operation lifetime

We found that hole diffusion in a centimeter-scale can be achieved in a PEDOT:PSS layer via composition and interface engineering. This ultralong distance hole diffusion enables substantially enhanced hole diffusion current in the lateral direction perpendicular to the applied electric field in typical organic optoelectronic devices. By introducing this lateral-hole-diffusion layer (LHDL) at the anode side of organic light-emitting diodes (OLEDs), both reduced efficiency roll-off and enhanced operation stability are demonstrated. In conventional OLEDs, balance in electron and hole currents is typically achieved by leakage of the major carrier through the devices or by accumulation of the major carrier inside the devices. Both of these are known to reduce performances leading to efficiency roll-off at high currents, reduction of operation stability due to exciton-polaron annihilation etc. The application of the LHDL provides a new strategy for current balancing with much reduced harmful effects from the previous two approaches. For example, by incorporating the diffusion layer in a white phosphorescent OLED, 94% of its maximum efficiency can be maintained even at a brightness of 10000 cd/cm 2 . At a high brightness of 30000 cd/cm 2 , external quantum efficiency of 13.9% without using any optical photon extraction layer. The OLED also show 5.5 times improvements in operation lifetime over the device without the diffusion layer. This study shows that centimeter-scale hole diffusion can be achieved in organic semiconductors and generally applied for enhancing efficiency and stability of OLEDs.

While full-color organic light-emitting diode (OLED) displays have been widely commercialized in the past decade, commercial products of OLED solid state lighting are still rare. One important reason is that OLEDs, especially high efficiency phosphorescent OLEDs, do have a common disadvantage that their efficiencies show significant roll-off at high brightness [1][2][3][4][5][6][7][8][9] . It is thus important to address this issue for promoting OLEDs' lighting applications. The "efficiency roll-off" issue is caused by different non-linear and complicated processes related to organic semiconductors' intrinsic properties, such as charge imbalance, bimolecular quenching processes and exciton dissociation induced by heat or electric field [9][10][11] . For organic semiconductors, hole drifting mobilities in hole-transporting materials are typically several orders of magnitude higher than electron mobilities in electron-transporting materials [9,10,12] . It is generally considered that such mobilities differences would lead to unmatched electron and hole currents. In fact, Fave et al have shown that there are two possible scenarios in typical OLEDs [13] . In the first situation, after electron-hole recombination, the surplus carriers (typically hole) will flow through the whole devices. These leakage currents not only waste energy without generating light, it can also decrease operation lifetime. For example, Aziz et al have shown that leakage of hole current can cause degradation of Alq3 in a prototypical NBP/Alq3 device [14] . In many high efficiency devices, hole-blocking layers are thus inserted to suppress the hole leakage current. This leads to the second scenario that excessive holes would accumulate inside the devices leading to built-in electric fields which would suppress the hole current and finally achieve balanced electron and hole currents.
However, these accumulated holes can form polarons and can quench excitons via excitonpolaron annihilation leading to decreased efficiency and operation lifetime [15][16][17][18][19][20][21][22][23][24] . It can be seen that in either scenario, both efficiency and operation lifetime are harmfully affected. The key question here is that before we can develop materials with matching electron and hole mobilities is there a third scenario beyond the above two described by Fave et al?
In this work, we show that a third scenario is possible via introducing current flow in the lateral direction (i.e. perpendicular to the applied electric field). So far almost all studies of OLEDs are mainly focused on the carrier dynamics along the direction of electric field; namely the drifting of carriers perpendicular to the planar devices [25][26][27] . However, charge carriers can also diffuse in all directions, including perpendicular to the electric field, as carrier "diffusion" is driven by concentration gradient and is independent of the electric field [28] . Recently, Leo et al for the first time constructed an electron lateral transport layer with a conductivity of 4 S/cm by doping C60 with 16 wt% of an electron donor material tetrakis (1,3,4,6,7,8-hexahydro-2Hpyrimido [1,2a] pyrimidinato)ditungsten (II) [W2(hpp)4], and observed emission spreading of ~300 μm outside the anode-cathode overlapping region [29,30] . Forrest et al later showed a breakthrough that lateral electron diffusion in centimeter scale can be achieved in a doped C60 channel at room temperature [31] . This centimeter-scaled electron diffusion is of critical importance for understanding fundamental physics in organic optoelectronic devices and can be applied for making charge coupled devices [32] . On the other hand, such long-range diffusion for hole has not be reported.
In this work, we demonstrated that hole diffusion in centimeter length scale can be achieved in PEDOT:PSS layers via composition and interface engineering. Such ultralong scale hole diffusion is further exploited to address the issue of efficiency roll-off in OLEDs. It was found that lateral hole diffusion beyond the cathode-anode overlapping region can redistribute carriers and induce additional electron injection from the cathode/organic interface. This leads to effective reduction of hole accumulation inside the device and thus reduces efficiency roll-off.
We demonstrate this by incorporating a lateral-hole-diffusion layer (LHDL) in a white phosphorescent OLED. 94% of its maximum EQE (EQEmax) can be maintained even at a high brightness of 10000 cd/cm 2 . The device also shows high EQE of 13.9 % at brightness of 30000 cd/cm 2 . To the best of our knowledge, this device shows one of the highest EQE at brightness beyond 30000 cd/cm 2 [33][34][35][36] . The device also shows over 5 times of operation lifetime enhancement comparing with the corresponding device without the LHDL.  Figure   S1 and Table S1). Relative EQE with respect to the maximum EQE (EQEmax) of the device is shown with  symbols in Figure 1a. It can be seen that EQE of the device decreases considerably when the current density is higher than 1 mA/cm 2 . Only about 20% of the EQEmax can be maintained when the current density is 600 mA/cm 2 . The significant EQE loss at high current densities in typical phosphorescent OLEDs have been attributed to triplet-polaron annihilation (TPA) and triplet-triplet annihilation (TTA) [9,10,18] . Following the approach of Leo et al [9] and with refer to the parameters ( Figure S2a and Table S2), we proceed to determine their relative contributions by analyzing densities of triplets (nT) and polaron (nP) at steady state.

Properties of conventional devices without lateral-hole-diffusion layer
Calculated relative EQE losses due to TTA and TPA are respectively shown as pink and cyan areas in Figure 1a. Calculated densities of triplet and polaron at different current densities are given in Figure S2b.
As shown in Figure 1a, TPA dominates the quenching process across the whole current range.
This phenomenon can be attributed to excessive hole accumulation caused by the unmatched hole and electron transporting abilities of the organic layers. To confirm this, we prepare a holeonly (C1h) and an electron-only (C1e) devices by modifying the structure of device C1 ( Figure   S3). Figure S4a shows that current density of device C1h is much higher than that of device C1e. From this result, it can be reasonably considered that the hole and electron transporting abilities of device C1 are highly unmatched (hole dominate). We then measured the capacitancevoltage characteristic of device C1 ( Figure S4b). It can be seen that upon carrier injection (at 2.8 V, point a'), capacitance of device C1 shows an initial increase as voltage increases. This is attributed mostly to holes accumulation in the emitting layer based on the discussion in Supplementary Note 1.
Using the "Marburg model'' ( Figure S5a) [13,37] , the reason of carrier accumulation in device C1 is explored in Supplementary Note 2. In the operating hole-dominant device C1 ( Figure   S5b), the recombination current IR can be expressed as: where, Ih and Ie are respectively the injected hole and electron currents at the electrode/organic interfaces. Ih' is the leakage hole current beyond the recombination zone. Qh is the accumulated hole charges inside the device. Due to efficient hole blocking abilities of TmPyPB, Ih' can be approximated to zero for device C1. Thus, the balance of hole and electron currents is mainly achieved via the term dQh/dt. Upon carrier injection ( Figure S5b), Qh increase steadily, such that internal potential distribution will be affected. The potential difference (Eh) across hole transport region will decrease, leading to a decreased Ih. Until finally, enough Qh is accumulated (ie. dQh/dt=0) and lead to a dynamic equilibrium between hole and electron currents (Ih=Ie).
Under this dynamic equilibrium, internal electric field distribution is highly uneven. For example, Fave et al showed that Ee can be over 3 times higher than Eh [13] . Given that the electric field for typical OLEDs is high (> 10 7 V/m), a considerable number of holes would accumulate in the device interior (l0 11~l 0 12 cm -2 , with refer to our result as shown in Figure S4b). The accumulated holes finally lead to serious TPA in device C1 (Figure 1a).

Design of the Lateral-hole-diffusion Layer
To address the issue of excessive hole accumulation, we proposed to introduce a lateral hole current IL by inserting a lateral hole transport layer (LHTL) between ITO and organic function layers, as shown in Figure 1b and 1c. The IL is anticipated to generate an additional electric field helping to extract electrons from the cathode side. As discussed in Supplementary Note 3, we show that after introducing the LHTL, it is possible to achieve hole-electron current balance without involving (or with much reduced) hole accumulation. However, Supplementary Note 3 also shows that the LHTL-induced current balance only works under the assumption that the lateral current IL is obtained via diffusion from the LHTL layer at the anode-cathode overlapping region instead of injection from the ITO. Further evidences supporting this assumption are provided in later parts of the paper.
PEDOT:PSS is exploited for applications as the lateral transport layer as its conductivity can be changed over a wide range by adjusting its composition and configuration ( Figure S6). can substantially decrease their resistivities. It is interesting to note that PEDOT:PSS has simultaneously high conductivity and capacitance (Figure 1d, 1e). In fact, holes can be stored at the interface between the conducting PEDOT rich phase and the insulating PSS rich phase [38,39] . Figure 1e shows that the capacitance of PEDOT:PSS can be increased over two orders of magnitudes upon treatments.
Devices C1, C2, D1 and D2 were then prepared using respectively PE4083, PE4083/PE8000, PE4083-MeOH and PE4083-MeOH/PE8000 as shown in Figure 1f. Figure 1g shows images of the devices operating at 6 V. It can be seen that the emitting area in devices C1 and C2 are limited to the cathode-ITO overlapping region. Apparent emission spreading out of the cathode-ITO overlapping region can be observed in devices D1 and D2. Apparently, the conductivities of PE4083 and PE4083/PE8000 layers are not high enough to allow adequate lateral hole current IL such that devices C1 and C2 behave as conventional devices with no observable emission spreading. The high conductivity of PE4083-MeOH and PE4083-MeOH/PE8000 in devices D1 and D2 enable enhanced lateral hole current IL and thus emission spreading. In particular, emission can still be obtained in device D2 from regions of centimeter-scale away from the cathode-ITO overlapping region. It can be noted that device D2 shows much wider emission spreading than device D1 (Figure 1g), although their PEDOT:PSS layers have similar lateral conductivities (~4 S/cm, Figure 1d). This suggests that the capacitance (Figure 1e) of the PEDOT:PSS layer might have influences on the lateral current IL. Thus, we further measure the lateral impedance spectra of the PEDOT:PSS layers in devices C2 a n d D 2 w i t h t h e configuration as shown in Figure S7. It can be clearly seen that the PH4083-MeOH/PH8000 film behaves as a Warburg short element ( Figure S8a), while the PH4083/PH8000 film behaves as a Warburg open element ( Figure S8b). This indicates that hole transport in the former (latter) layer belongs to a finite-length diffusion with transmissive (reflective) boundary [40] . The hole diffusivity, D, of the PE4083-MeOH/PE8000 film is then estimated as ~3×10 -3 c m 2 /s (Supplementary Note 4), which is nearly two orders of magnitude higher than that (~3×10 -5 cm 2 /s) of the PE4083/PE8000 film. We can thus reasonably consider that lateral carrier Transient EL from device D2 was then measured from the spot marked as with "*" in Figure   1g which is about 0.57 cm outside the cathode-ITO overlapping region using a longer electrical pulse of 480 μs ( Figure S9). It is interesting that no appreciable EL signal can be observed before 90 μs (see magnified region in the inset of Figure S9). This suggests that emission from this spot requires diffusion and accumulation of carriers from a long distance away. Thus, the initial and delayed emissions shown in Figure 2a   the delayed EL rise is not directly injected from the ITO anode. The delayed EL can be more reasonably explained by lateral hole diffusion in the PEDOT:PSS layer driven by the hole concentration gradient. When the bias is first applied, carrier movement will be dominantly controlled by the vertical electric field. There will be little lateral current IL as there is no apparent carrier density gradient initially. The PEDOT:PSS will be steadily charged up with an increasing hole concentration. Upon fully charged, there will be a large enough lateral hole concentration gradient driving a lateral hole current IL. The laterally diffuse holes would then induce additional electron injection from the cathode giving rise to the delayed EL. With this understanding, the hole-electron current balance can be achieved via lateral hole diffusion (as discussed in Supplementary Note 3): (2).
The term refers to lateral hole diffusion, and A is the longitudinal cross-section area of the LHDL at the border (dash line in Figure 1c) of the ITO-cathode overlapping region.
To further confirm this, capacitance-voltage characteristics of the devices and currentvoltage characteristics of their single-carrier devices ( Figure S10) were measured. As shown in Figure 2c and S11, devices D1 and D2 show much higher geometric capacitance than devices C1 and C2. This is due to highly improved carrier storage ability of the PEDOT:PSS layers upon MeOH treatment ( Figure S12 and Supplementary Note 5). After carrier injection (point a/a' in Figures 2c and S11, and dotted line in Figure 2d), devices C1 and C2 show capacitance increases from point a' to point b', corresponding to carrier accumulation in the emitting layer [41] . Interestingly, the capacitance changes in devices D1 ( Figure S11) and D2 (Figure 2c) differ considerably from those of devices C1 and C2. It can be seen that upon turning on (at 3.1 V, blue sphere/point b), capacitances of devices D1 and D2 show initial decreases as voltage increases. This gives an evidence that current balance in these devices is not solely achieved via carrier accumulation ( ), and the lateral current IL should work for achieving current balance ( ). Furthermore, the lateral diffusion of hole makes it possible for achieving current balance without suppressing hole current. As shown in Figure 2d, the current of device D2 (D1) is much higher than that of device C2 (C1) under high bias voltages. According to the voltage-current characteristics (Figure 2e and S13) of single carrier devices, the current improvement of devices D2 and D1 is mainly attributed to the improvement in electron current (see IeL in Figure S5c).
Results from the device characteristics also support the influence of the lateral current IL. We can note that performances of devices D2 and D1 are enhanced at high current ( Figure S1). As current increases, device D2 (D1) shows much less EQE roll-off (Figure 2f) than device C2 (C1). A brightness enhancement within the ITO-cathode overlapping region of devices D2 and D1 is also observed ( Figure S14). These results support the reduction of TPA within and outside the ITO-cathode overlapping region of devices D2 and D1.
Working mechanism of an OLED with a LHDL As noted above, a working mechanism of the OLEDs with LHDL is proposed and shown in area, the total luminescence of device D2 is much higher than that of device C2 ( Figure S1b).
Due to the reduced hole accumulation in the emitting layer, TPA inside the ITO-cathode overlapping region is also reduced and thus resulting in a brightness enhancement inside the nominal device region ( Figure S14).

OLEDs with lateral-hole-diffusion layers and ITO array anodes
As shown in Figure S15, the emission intensity shows an exponential decay with the distance outside the ITO-cathode overlapping region. This agrees well with the assumption that the lateral current IL is due to diffusion from the PEDOT:PSS layer ( Figure S16 and Supplementary Note 6). To achieve quasi-uniform emission, application of the hole lateral diffusion for OLEDs is then developed by using an array of ITO grid anode (Figure 4a). Width of and spacing between the ITO fingers are shown in Figure S17. Device with the structure of device D2 was then fabricated on substrates with the ITO arrays and labelled with device D2AA'. The impedance spectra ( Figure S18) and infrared images ( Figure S19) show that the use of long and thin ITO array will not result in increased ITO resistance nor serious thermal effect. This is due to parallel circuit characteristics of this type of ITO electrode. Figure 4b shows image (upper) of operating device D2AA'. Region marked with green circle is shown as magnified image (lower). It can be seen that overlapping of spread-out emissions from neighboring ITO finger eventually smooth out the intensity modulation and the fringe pattern is no longer observable in device D2AA'. (61.0% of its EQEmax). According to the EL spectra ( Figure S21), shifting of emission spectra partly contribute to the extreme small efficiency roll-off in device WDAA'. Considering the higher proportion of yellow emission in WCAA' (see inset of Figure 4d), it is reasonably concluded that the lateral hole diffusion is the main cause of the efficiency enhancement in WDAA'. This strategy is not only specific to the devices above but represents a universal strategy that can be applied in different types of OLEDs (i.e. include blue, red phosphorescent devices, and TADF devices) for improving performances under high current ( Figure S22 and Table S3).
More interestingly, the hole diffusion layer is also beneficial for improving operational lifetime of phosphorescent OLEDs. As shown in Figure 4e, the LT50 lifetime (time to 50% of initial brightness of 1000 cd/m 2 ) of device WDAA' can attain 149 hours, corresponding to 5.5 times improvements compared to device WCAA'. Similar improvement can also be observed in blue device BDAA', compared with device BCAA' ( Figure S23). Lifetime improvements of the blue and the white OLEDs with LHDLs should be attributed to the reduction of excitonpolaron annihilations in such devices, which are well known as a main reason for the short operational lifetime of phosphorescent OLEDs [24] .
In conclusion, centimeter-scale hole lateral diffusion behavior is observed in a PEDOT:PSS bilayer film which consists of a methanol treated PEDOT:PSS layer with high conductivity which form a highly capacitive interface with another untreated PEDOT:PSS layer. With this hole-diffusion layer, hole injected from the anode can diffused laterally in centimeter scale away from the anode. This process (1) generates spatial variation of carrier density for balancing carrier injection/transport in the normal emission region defined by the ITO-cathode overlapping area and (2) induces additional electron injection outside the ITO-cathode overlapping area. These not only lead to a higher luminescence resulting from the spread-out emission and also substantially reduce exciton loss due to polaron-exciton quenching due to the reduced excess hole density at the normal emission region. By combing this hole-diffusion layer with an ITO grid array anode, we demonstrate high performance phosphorescent OLEDs with record low EQE roll-off at high brightness and much improved device lifetime.

Conflict of Interest:
The authors declare no conflict of interest.

Supplementary Files
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